Kaosar and M(ex+od)#12362
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Kaosar and M(ex+od)

1 second
256 megabytes
Hard

You are given integers and you have to print a permutation of \{1,2,...,n\}.

such that

\large \mathop{\text{MEX}}\limits_{i=1}^{n-1} (p_i \bmod p_{i+1})

is exactly or say there is not any valid permutation.

use randomized algorithm

Here denotes Minimum Excluded Integer.

Input

The first line of contains a single integer (1\le t\le 10^3) — the total number of test cases.

In each test case there will be two integers (2\le n\le 10^5) and (0\le k\le 10^9) — the length of the permutation and the desired .

It's guaranteed that \sum n \le 10^6 overall tests.

Output

If there is a valid permutation then print it and if there isn't any valid permutation then print .

Examples

Example 1

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Note

In first test case \text{MEX}(1\mod 2)=0

Scoring

  1. Subtask ( points) : (k<2)

  2. Subtask ( points) : (n\le 8)

  3. Subtask ( points) : No additional constraints.